A lesson on thales' theorem viewed from the specialized teacher's knowledge

Abstract

Abstrac: This paper presents the analysis of an observed lesson on Thales's Theorem in a Chilean secondary school, using the Mathematics Teacher's Specialised Knowledge (MTSK) model. We consider various aspects of the teacher's specialised knowledge with respect to Thales's Theorem itself, as an element of teaching and learning, and to demonstrations, as a mathematical practice, in general. From this analysis, and guided by the Chilean syllabus requirement for this topic, we construct a snapshot of the interrelated elements of knowledge deployed by the teacher, which enables us to account for how he brings particular aspects into focus. The findings show that the utility which he attaches to the theorem, that of being able to apply it, alongside his view of it as a result of similarity and his emphasis on a numerical approach, is closely linked to his knowledge of registers, the interconnections he makes with other content items, his use of resources, the kind of tasks he sets up, and the knowledge of mathematical practices he makes evident.